L-GCNs learn from complex multigraphs, improving node classification performance.
problem Learning from complex multigraphs with rich edge labels.
method Latent-Graph Convolutional Networks (L-GCNs) that propagate information to a latent adjacency tensor.
result L-GCNs improve node classification performance, especially with nonlinear interactions.
AMES framework selects optimal embedding space for latent graph inference.
problem No principled method for choosing the best embedding space for latent graph inference.
method Differentiable AMES framework using backpropagation to select optimal embedding space.
result Consistently achieves comparable or superior results across multiple datasets.
Study neural architectures on learned latent graphs using Schrödinger dynamics.
problem Understanding neural architectures on learned latent graphs.
method Optimizes over stratified moduli space of weighted graphs with Kähler-Hessian metric.
result Multilayer stationary networks are equivalent to global stationary problems on supra-graphs.
New method learns graph structure and uncertainty from data.
problem Learning latent graph structures and their uncertainty from data.
method Proposes a sampling-based method to learn latent graph structure and uncertainty simultaneously.
result Proves that suitable loss functions on stochastic model outputs solve both learning latent graph structure and achieving optimal predictions.
Variational autoencoder models dynamic latent graphs for neural point processes.
problem Modeling event dynamics with changing trends over time.
method Sequential latent variable model with dynamic latent graphs.
result Higher accuracy in predicting inter-event times and event types.
GLAD improves latent graph generation by quantizing discrete latent space.
problem Latent space graph generative models lack performance and make unnatural assumptions.
method Adapting diffusion bridges to a discrete latent space, avoiding data space decompositions.
result GLAD achieves competitive performance on graph benchmark datasets.
FMI uses matching to mimic interventions for causal feature learning.
problem Challenges in causal discovery from observational data.
method Feature Matching Intervention (FMI) using matching to emulate perfect interventions.
result FMI outperforms in identifying causal features from observational data.
Identifies directed graphs from node measurements using polynomial filters.
problem Inferring directed network topology from nodal measurements.
method System identification of graph convolutional filter followed by topology inference.
result Effective recovery of directed graphs from measurements.
New framework estimates graph from multimodal functional data.
problem Estimating graph from joint multimodal functional data.
method Integrative framework using partial correlation operator.
result Estimator converges to stationary point with quantifiable error.
Proposes SDE framework for uncertainty quantification in graph neural networks.
problem Lack of uncertainty quantification in graph neural networks.
method Introduces Latent Graph Neural Stochastic Differential Equations (LGNSDE) with Bayesian prior-posterior mechanism and Brownian motion.
result LGNSDEs provide theoretically sensible guarantees for uncertainty estimates and are robust to perturbations.
Convolutional networks outperform fully-connected ones in certain tasks.
problem Understanding the computational advantage of convolutional networks over fully-connected networks.
method Demonstrated a computational advantage through a specific problem class.
result Convolutional networks can solve certain problems that fully-connected networks cannot, even with gradient descent.
PGNs dynamically infer and use graph structures to improve model generalization.
problem Static graph structures inferred by machine learning practitioners are often suboptimal for tasks.
method PGNs augment graphs with dynamically inferred pointers for improved model generalization.
result PGNs outperform unrestricted GNNs and Deep Sets on dynamic graph connectivity tasks.
Convolutional Neural Networks, as most artificial neural networks, are commonly viewed as methods different in essence from kernel-based methods. We provide a systematic translation of Convolutional Neural Networks (ConvNets) into their kernel-based counterparts, Convolutional Kernel Networks (CKNs), and demonstrate th…
VC dimensions of group CNNs are infinite for certain kernels and groups.
problem Estimating the generalization capacity of group convolutional neural networks.
method Identifying precise VC dimension estimates for simple sets of group CNNs.
result Two-parameter families of convolutional neural networks have an infinite VC dimension for infinite groups and certain kernels.
We introduce Group equivariant Convolutional Neural Networks (G-CNNs), a natural generalization of convolutional neural networks that reduces sample complexity by exploiting symmetries. G-CNNs use G-convolutions, a new type of layer that enjoys a substantially higher degree of weight sharing than regular convolution la…
We describe convolutional networks using harmonic functions.
problem Understanding the function space and smoothness of convolutional networks.
method Using reproducing kernel Hilbert spaces and functional ANOVA decomposition.
result Convolutional networks can be decomposed into a sum of elementary functions.
Enhances group convolutional networks with attention to learn meaningful relationships.
problem Lack of explicit means to learn meaningful relationships among symmetry patterns.
method Introduces attentive group equivariant convolutions, applying attention during convolution.
result Consistently outperforms conventional group convolutional networks on benchmark datasets.
Automates graph convolutional network design for semi-supervised node classification.
problem Designing optimal graph convolutional network architectures for semi-supervised node classification.
method An automatic process to define a problem-specific architecture based on graph structure.
result The proposed method outperforms existing methods in classification performance and network compactness.
Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network (TAGCN), a novel graph convolutional network defined in the vertex domain. We provi…
Convolutional networks struggle with repeating patterns in ECGs.
problem Modeling repeating patterns in electrocardiogram signals.
method Demonstrated through ECG examples, highlighting systemic issues in deep learning.
result Counterintuitive effects on generalization in deep networks.
Convolutional neural networks converge quickly with gradient descent.
problem Learning efficient image classifiers with over-parameterized networks.
method Gradient descent for training over-parametrized CNNs with global average-pooling.
result Gradient descent quickly reduces the misclassification risk of CNNs.
Traffic forecasting is a particularly challenging application of spatiotemporal forecasting, due to the time-varying traffic patterns and the complicated spatial dependencies on road networks. To address this challenge, we learn the traffic network as a graph and propose a novel deep learning framework, Traffic Graph C…
Proves DCNNs with expansive convolution are strongly universally consistent.
problem Theoretical consistency of deep convolutional neural networks (DCNNs).
method Empirical risk minimization on DCNNs with expansive convolution (with zero-padding).
result DCNNs with expansive convolution are strongly universally consistent.
This work proposes hyperbolic deep convolutional neural networks for better pattern recognition.
problem The limitations of Euclidean deep convolutional neural networks in capturing intricate patterns.
method Developed Hyperbolic DCNN based on Poincaré Disc, analyzing expansive convolution in non-Euclidean space.
result Hyperbolic convolutional architecture outperforms Euclidean ones in pattern recognition tasks.
New multigrid approach reduces CNN parameters by focusing on structured convolutions.
problem Redundancy in standard CNNs leads to high parameter count.
method Replace standard convolutions with structured multilevel convolutions.
result Linearly proportional number of parameters to network width, no loss in accuracy.
Convolutional neural networks improve image classification accuracy.
problem Improving accuracy in image classification.
method Analyzing the convergence rate of misclassification risk for image classifiers.
result A rate of convergence independent of image dimension proves the effectiveness of CNNs.
Random convolutional networks can be fooled with adversarial examples.
problem Existence of adversarial examples for random convolutional networks.
method Utilizing isoperimetric inequalities on the special orthogonal group so(d). result Adversarial examples exist for various random convolutional networks.
L-CNNs learn gauge invariant quantities on lattices.
problem Learning gauge invariant quantities on lattices.
method Novel convolutional layer preserving gauge equivariance and forming Wilson loops.
result L-CNNs can approximate any gauge covariant function on the lattice.
New bounds for CNNs show better generalization than previous models.
problem Improving understanding of CNNs' generalization ability.
method Proposed tighter generalization bounds for CNNs by exploiting the sparse and permutation structure of weight matrices and spectral norms of convolution operations.
result Theoretical and experimental results show tighter bounds for CNNs than existing bounds.
Convolutional networks can denoise images without training data.
problem Denoising and regularization of images without labeled data.
method Exploiting the structural bias of convolutional generators through gradient descent.
result Early-stopped gradient descent denoises/regularizes images effectively.
In this paper we cast the well-known convolutional neural network in a Gaussian process perspective. In this way we hope to gain additional insights into the performance of convolutional networks, in particular understand under what circumstances they tend to perform well and what assumptions are implicitly made in the…
New method prevents gradient attenuation in Lipschitz constrained convolutional networks.
problem Gradient norm attenuation in Lipschitz constrained convolutional networks.
method Block Convolution Orthogonal Parameterization (BCOP) to train scalable, expressive, provably Lipschitz convolutional networks.
result Empirically, BCOP parameterization is competitive with existing approaches to provable adversarial robustness and Wasserstein distance estimation.
This research studies affine invariance in continuous-domain convolutional neural networks.
problem Recognizing patterns and features under affine transformations in continuous domains.
method Introduces a new criterion for assessing affine invariance, embeds images into the affine Lie group, and analyzes convolution over this group.
result Extends the scope of geometrical transformations that deep-learning pipelines can handle.
Proposes a new convolutional neural network for non-grid data.
problem Limited applicability of standard CNNs to non-grid structured data.
method Introduces Parametric Continuous Convolution (PCC) with learnable kernel functions.
result Significant improvement in point cloud segmentation and lidar motion estimation.
Deep neural network predicts traffic flow on city maps.
problem Short-term traffic flow prediction on high-resolution city maps.
method UNet-based deep convolutional neural network with densely connected layers.
result Best performance on the Traffic4cast challenge 2019.
Convolutional neural network is an important model in deep learning. To avoid exploding/vanishing gradient problems and to improve the generalizability of a neural network, it is desirable to have a convolution operation that nearly preserves the norm, or to have the singular values of the transformation matrix corresp…
Previous research has shown that computation of convolution in the frequency domain provides a significant speedup versus traditional convolution network implementations. However, this performance increase comes at the expense of repeatedly computing the transform and its inverse in order to apply other network operati…
Graph convolutional networks fail to use eigenvectors beyond the first, unlike spectral embedding.
problem Understanding when graph convolutional networks fail compared to spectral embedding.
method Presented a simple generative model to illustrate failure.
result Graph convolutional networks fail to use eigenvectors beyond the first in certain graphs.
We applied pre-defined kernels also known as filters or masks developed for image processing to convolution neural network. Instead of letting neural networks find its own kernels, we used 41 different general-purpose kernels of blurring, edge detecting, sharpening, discrete cosine transformation, etc. for the first la…
Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural network architectures remains highly fragmented impeding the development of optimized …
Deep convolutional neural networks trained on large datsets have emerged as an intriguing alternative for compressing images and solving inverse problems such as denoising and compressive sensing. However, it has only recently been realized that even without training, convolutional networks can function as concise imag…
The fully connected layers of a deep convolutional neural network typically contain over 90% of the network parameters, and consume the majority of the memory required to store the network parameters. Reducing the number of parameters while preserving essentially the same predictive performance is critically important …
Graph convolutional kernel networks generalize CNNs to graph data.
problem Representing graph-structured data for machine learning.
method Convolutional kernel networks applied to graph data.
result Competitive performance on graph classification benchmarks.
Fully convolutional neural networks (FCN) have been shown to achieve state-of-the-art performance on the task of classifying time series sequences. We propose the augmentation of fully convolutional networks with long short term memory recurrent neural network (LSTM RNN) sub-modules for time series classification. Our …
Coordinate-independent convolutions on manifolds avoid reference frame ambiguity.
problem Applying convolutions on non-Euclidean manifolds without reference frame ambiguity.
method Developed coordinate-independent and gauge-equivariant convolutions on Riemannian manifolds.
result Coordinate-independent convolutions are equivariant under local gauge transformations.
L-CNNs maintain gauge symmetry on non-Abelian lattice theories.
problem Applying convolutional neural networks to non-Abelian lattice gauge theories while preserving gauge symmetry.
method Developed a geometric formulation of L-CNNs that are equivariant under global symmetries and gauge transformations.
result Convolutional operations in L-CNNs are a specific case of gauge-equivariant neural networks on SU(N) principal bundles. Recently, many researchers have been focusing on the definition of neural networks for graphs. The basic component for many of these approaches remains the graph convolution idea proposed almost a decade ago. In this paper, we extend this basic component, following an intuition derived from the well-known convolutional…
Graph Convolutional Networks improve performance on complex data.
problem Processing high-dimensional, graph-based data for automation.
method Enhanced existing Graph Convolutional Network models with four improvements.
result Significant performance improvements on four benchmark datasets.